[Cartman]: “Kyle, all those times I called you a stupid Jew, I didn’t mean it – you’re not a Jew.”

[Kyle]: “Yes I AM, Cartman! I AM a Jew!”

[Cartman]: “No, no, don’t be so hard on yourself.”

–Exchange between Cartman and Kyle, South Park: Bigger, Longer, and Uncut

It has occurred to me that multi-variable calculus can serve as a potent metaphor for certain kinds of reasoning.

In single-variable calculus, the equations you deal with are simple: one variable is defined in terms of a series of mathematical operations applied to another. When graphed in a Cartesian system, the result is a line embedded in a plane. Direct, elegant, uncomplicated. The techniques for determining the slope of that line at any point are relatively straightforward, so that form of calculus is the one people learn first.

When you’re dealing with more than two variables, when one variable is defined in terms of operations applied to two or more, things get a little more complex. The simplest case involves three variables, and the result is often a surface embedded in a space. The methods you were taught in single-variable calculus can’t be applied to those equations.

One of the things you’re taught to do is take the original equation and rewrite it, treating all but one of the operational variables as constants each time. The standard techniques can then be applied to the modified versions of the equation. Essentially, you’re talking cross-sections through the surface in the Cartesian space along different directions, and determining the slope of the surface in a particular direction.

To measure the slope in terms of any variable, you must treat the others as constants.

There’s a certain kind of logic that operates in much the same way. We have beliefs about the world, and we compare those beliefs to incoming data from the world. We can hold those beliefs constant, or we can be uncertain as to their validity; we can accept the data as accurate and representative, or we can be uncertain as to its accuracy and representativeness. If we let the status of both the beliefs and the data vary, we cannot evaluate either.

The quoted exchange above is an excellent example of this phenomenon cast in a humorous light. For context: Cartman is a vile and bigoted child whose innate charisma barely serves to compensate for his many prejudices. He has an established set of ideas about what properties are associated with the concept of ‘Jewishness’ – various negative and unflattering ones. One of his friends, Kyle, is Jewish. Cartman frequently needles Kyle about being Jewish, much to Kyle’s annoyance, but in truth he recognizes that Kyle has a variety of laudable traits.

So: what are the variables? Kyle’s properties, and the properties of the concept.

Cartman’s idea of what Jews are like is incompatible with his observations of what Kyle is like. He must therefore hold one variable constant and set its value, while letting the other vary and determining its value in relation to the set given. The humor comes from the contrast between our expectations and what actually happens: the cliche is that the bigoted individual learns to reject his prejudices by interacting with a member of the group he prejudges, but Cartman does the opposite and instead denies that his friend is actually a member of the despised group. Instead of adapting his ideas about Jews to fit Kyle’s identification with them, he adapts his ideas about Kyle’s identification and holds fast to his prejudices.

This illustrates a very important point: The manner in which we decide which of the variables to accept as a constant given determines much about what conclusions we derive from them.

If we accept the data, we must let our evaluation of our beliefs teeter, with the data determining which way the outcome leans. If we accept the beliefs, we must let our evaluation of the data teeter, with our beliefs determining which way our thinking tips. One or the other must be held constant. How we decide which will be conserved and which will be altered depends on our evaluation of each.

If we have a well-established way of thinking, one that has served us well and endured many challenges, we are not likely to abolish it due to some contrary evidence. We are far more likely to dismiss the evidence as a fluke or error because it is incompatible with our existing theory. Logically, the conclusion could go either way: rejecting the theory or rejecting the evidence. In practice, it takes a great deal of evidence that we are unable to reject to overturn the theory, and unless a very high standard of proof is met, we reject the evidence every time.

One of the tasks of the rationalist is to always hold back from reaching definitive conclusions, to let the inclusion of this and the exclusion of that be merely provisional. Human beings aren’t good at this – when we note that something is incompatible with our understanding, we tend to reject it completely, deleting it from our awareness. It takes effort and resources to keep track of the possibilities we exclude, and it’s far easier to abolish them. But this tends to prevent us from storing up enough evidence to overturn our theories – each is evaluated individually, instead of collectively, and so a mass of data that might force us to change our minds is rejected one part at a time.

Rationalists must balance atop the see-saw, maintaining equilibrium, identifying and countering inclinations to lean one way or the other, always sensitive to changing conditions and ready to react appropriately.

Not only does submitting a new post take up to half-an-hour with the connection I have available, but I’m not feeling too well.

Last night I took a closer look at the two-week old bottle of olive oil in my fridge and noticed that the bottom inner surface looks like a petri culture medium. As I had recently used that oil to prepare my dinner, I am now otherwise occupied with trying to ensure that my internal organs do not become external.

I would wonder what was wrong with that particular bottle that caused the oil to spoil so rapidly, but I have other concerns at the moment.

I for one cannot help but be struck by the contrast between our government’s ‘generous’ distribution of massive amounts of money to various financial institutions, much of which has gone to pay dividends to investors and supply executive compensation instead of what the politicians hoped but did not require the banks to use it for, and the relative stinginess of Washington to lend, much less give, money to the American automakers.

Perhaps part of the problem is that the American groupmind has long accepted American automakers as producing inferior products and services, even while they may have corrected this fault, while the people want to believe American financial institutions are hale and merely going through a rough patch. Detroit has a bad reputation, whether it still deserves it or not, and we desperately want Wall Street to have a good reputation whether it deserves it or not.

To be accorded that status is to be held blameless; once it has been granted, no one may suggest that the victim’s own choices might have contributed to the harm they suffered, nor may anyone suggest that the victim may have had the power to prevent by some means harm done to them. Suggesting that the harm may have been rightful or fair is out of the question; victims are those who have been wronged, those treated unjustly. If they weren’t wronged, they wouldn’t be victims, and since they are victims, they must have been wronged.

Once the status is granted, alternatives contrary to that status arising are automatically dismissed. Of course they weren’t responsible – they’re victims. Of course they were helpless – they’re victims. In logic, sufficient contrary evidence overturns an assertion, but mere logic does not apply to social consensus. If someone is defined as being a victim, everything must proceed from that given; questioning that definition is an attempt to undermine the social order and is evil in itself, and probably another attempt to harm the victim.

To be perceived as powerless and harmed, according to the consensus of our society, is to become entitled. Entitled to the sympathy and aid of the powerful. Entitled to the absence of contempt. Entitled to unique treatment; entitled to private, generous rulings that do not apply to others. As a consequence, gaining the status of victim brings immense power, a sort of aristocracy of the least and worst.

A sort of schizophrenic thinking takes hold in the people who want to acquire the status of victim for their favored group. For example, you can see it in a particular strain of feminists. They cannot accept that female genital mutilation is mandated and often carried out primarily by women; nor can they accept that lesser but similarly harmful fashions stem from women’s standards. Women are victims; ergo, they cannot be responsible for systematic oppression. The judgment of other women cannot possibly be involved; conformity to harmful standards cannot possibly be imposed by other women. Therefore, the odious cultural forces responsible for maintaining these atrocity must spring from men.

Not only is this sort of thinking untrue and thus harmful in itself, but it turns the assignment of responsibility into an even greater minefield that it would otherwise be.

If even Naomi Wolf voted for Obama, despite believing that his voting record is unacceptable, because he’s “the lesser evil”, no one ever’s going to refuse to take the least-worst option offered to them.

As of May 2004, my take on Friendliness is that the initial dynamic should implement the coherent extrapolated volition of humankind.

In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted.

Fascinating stuff. Where is this concept discussed in non-poetic terms? Where is it operationalized? There’s a whole long section in the original paper discussing the idea. Surely there must be some rigorous defining in there somewhere.

Locating it is left as an exercise for the reader, if you enjoy wild goose chases.

Let’s take a closer look at that name. ‘Coherent’ seems straightforward enough – in the context of abstract ideas, it means something along the lines of ‘logically connected; consistent’ or ‘having a natural or due arrangement of parts; harmonious’. Do humans, either individually or collectively, possess a coherent set of preferences? I have no idea how we could determine that. Judging from his writings, neither does Eliezer – but that’s not an obstacle. Eliezer doesn’t even bother to handwave the problem away – he simply ignores it.

‘Extrapolated’ is easy to grasp, as well. It has a clear definition: “to infer an unknown from something that is known”; in mathematics, it’s even clearer: “to estimate a function that is known over a range of values of its independent variable to values outside the known range”. Obviously human morality varies in a predictable way with the independent variable of time. Once, the concept of slavery was widely accepted, then the idea that it was intolerable spread itself, and now it’s abolished and we consider slavery repugnant. Clearly that’s progress because the unacceptable moralities past slowly developed into a form compatible the moralities of today. That form: the moralities of today.

Saith Eliezer:

Humanity’s moral memes have improved greatly over the last few thousand years. How much farther do we have left to go?

They have? I wasn’t aware that moral codes have improved greatly. How, precisely, do we evaluate a moral code other than by appealing to the one we’ve already accepted and internalized? Certainly there are standards of logic and self-consistency that don’t require us to make moral judgments, but my intuition tells me that’s not what Yudkowsky is talking about.

As for “how far we have left to go”, I’m not sure what to make of it. It’s as though he believes there’s some ultimate goal or teleological standard towards which humanity is collectively approaching. Peculiar, since human societies show every sign of adapting themselves to according to the conditions in which they exist, and evolutionary principles are notoriously not goal-driven.

By the standards of today, the standards of today are an improvement over the past. They’d have to be, because moral standards are necessarily applicable to standards in the abstract or general sense, and every system of standards that is self-consistent will view itself as a perfect match to its criteria for the ideal system of standards.

It is undeniable that moral conventions have changed, ‘progressed’ in the weak sense, to become what they are today. It is not clear that this change is orderly or predictable. Nor is it clear that today’s conventions are fundamentally superior to those of the past in any non-trivial sense, much less that they represent objective progress. There is a deplorable tendency of human beings to regard their present beliefs and positions, no matter how arbitrary, as being the end stage of a tremendous process of improvement. Man measures all things, and he tends to hold himself up as the standard of correctness. Unfortunately, even a little thought is sufficient to convince that we are in no sense an end stage, and that considering our prejudices and tendencies to be ultimate and defining truths is nothing more than pernicious narcissism.

You cannot extrapolate a random walk. Can we extrapolate moral change? I know of no proof that such a thing is possible, much less attainable for us. Does Eliezer offer that proof, or even a credible argument in favor of that possibility? Or does he merely take it for granted as an unquestioned assumption?

Where are the questions he claims I am bringing up as my own? Does he ask them? Or does he simply assert the answers he wishes to find as self-evident truths? To ask a question, you must not believe you already know the answer; if you have a belief, it must be set aside for the asking to occur. Does Eliezer set aside his beliefs so that he can ask honestly?

Read Yudkowsky’s writings. Take the time to look up his later writings if you wish, although I am not aware of any fundamental change in their content. You will have to judge for yourself, but I think you can guess the answer I found when I looked for one.